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The number of regions inside a 4-pointed star formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
2

%I #11 Apr 09 2021 01:02:33

%S 56,816,6064,18152,52088,100608,208168,336840,579136,846560,1310960,

%T 1784888

%N The number of regions inside a 4-pointed star formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

%C The star consists of a central square surrounded by four equilateral triangles. See the linked images.

%H Scott R. Shannon, <a href="/A338002/a338002.png">Image of the star with edge-count coloring for n=1</a>.

%H Scott R. Shannon, <a href="/A338002/a338002_1.png">Image of the star with edge-count coloring for n=2</a>.

%H Scott R. Shannon, <a href="/A338002/a338002_2.png">Image of the star with edge-count coloring for n=3</a>.

%H Scott R. Shannon, <a href="/A338002/a338002_3.png">Image of the star with edge-count coloring for n=4</a>.

%H Scott R. Shannon, <a href="/A338002/a338002_4.png">Image of the star with edge-count coloring for n=5</a>.

%Y Cf. A338003 (number of vertices), A331906, A331908, A007678, A092867, A331452.

%K nonn,more

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Oct 06 2020

%E a(8)-a(12) from _Lars Blomberg_, Apr 08 2021